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- 01GP3YFJ87KV2ZKET1X9NH5PJ8 classification A1.
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 date "2022".
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 language "eng".
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 type journalArticle.
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 hasPart 01GP3YGS40G691RWW1F0CSP7R1.pdf.
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 hasPart 01GRRKTZ7YR0X6GE8W47VHH2NB.pdf.
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 subject "Mathematics and Statistics".
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 doi "10.1007/s00145-022-09435-1".
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 issn "0933-2790".
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 issn "1432-1378".
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 issue "4".
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 volume "35".
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 abstract "In this paper, we use genus theory to analyze the hardness of the decisional Diffie-Hellman problem for ideal class groups of imaginary quadratic orders acting on sets of elliptic curves through isogenies (DDH-CGA). Such actions are used in the Couveignes-Rostovtsev-Stolbunov protocol and in CSIDH. Concretely, genus theory equips every imaginary quadratic order O with a set of assigned characters chi : cl(O) -> {+/- 1}, and for each such character and every secret ideal class [a] connecting two public elliptic curves E and E' = [a] * E, we show how to compute chi([a]) given only E and E', i.e., without knowledge of [a]. In practice, this breaks DDH-CGA as soon as the class number is even. which is true for a density 1 subset of all imaginary quadratic orders. For instance, our attack works very efficiently for all supersingular elliptic curves over F-p with p 1 mod 4. Our method relies on computing Tate pairings and walking down isogeny volcanoes. We also show that these ideas carry over, at least partly, to abelian varieties of arbitrary dimension. This is an extended version of the paper that was presented at Crypto 2020.".
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 author B9794F4C-8ACB-11E3-9069-E2B710BDE39D.
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 author urn:uuid:cf29833f-ea39-4bbd-8274-2413735e4f32.
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 author urn:uuid:f0fd857e-f7f7-457c-aa33-09a3cd67f9a0.
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 dateCreated "2023-01-06T16:26:32Z".
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 dateModified "2024-07-09T07:44:37Z".
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 name "Breaking the decisional Diffie–Hellman problem for class group actions using genus theory : extended version".
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 pagination urn:uuid:41c9c65b-4ecd-4329-ae63-025d8f45df70.
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 sameAs LU-01GP3YFJ87KV2ZKET1X9NH5PJ8.
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 sourceOrganization urn:uuid:785009ba-3238-47af-b9d0-c3bd7597ffd3.
- 01GP3YFJ87KV2ZKET1X9NH5PJ8 type A1.